A convenient procedure for digitally determining the magnitude of an unknown resistance resides in connecting same in circuit with a fixed capacitance to form an RC network whose time constant is a function of that resistance. A network of this type may be used in a one-shot pulse generator, such as a monostable multivibrator (monoflop) or univibrator, to establish a gating period whose duration T, depending on that time constant, is measured by counting the number of pulses emitted with a recurrence period t in the course of this period by a free-running oscillator, such as an astable multivibrator or flip-flop. When the unknown resistance element is replaced by a known calibrating resistance, the ratio T/t changes in accordance with the relative magnitudes of the two resistances. The same result can be had by using a gating-pulse generator of fixed duration T and varying the recurrence period t by alternately inserting the known calibrating resistance and the unknown resistance in an RC network forming part of the counting-pulse generator.
In the first instance, the duration T' of a gating period is given by EQU T'=R'.multidot.C.multidot.Q' (1)
where R' represents either the known calibrating resistance or the unknown resistance to be measured, C is the fixed capacitance and Q' is the natural logarithm of a constant taking into account the switching thresholds of the pulse generator. Thus the number N' of counting pulses generated during period T' is given by the relationship EQU N'=(T'/t')=f'.multidot.R'.multidot.C.multidot.Q' (2)
where f'=1/t' is the repetition frequency or cadence of the counting pulses.
In the second instance, with the gating period having a fixed duration T" and with the cadence of the counting pulses determined by the magnitude of the resistive branch of the RC network in the free-running pulse generator, that cadence is given by the relationship EQU f=(1/t")=(1/R".multidot.C.multidot.Q") (3)
where t" is the variable counting-pulse cadence, R" again represents either the unknown resistance or the calibrating resistance, and Q" is the natural logarithm of a constant based on the switching thresholds of the astable circuit. The pulse count N" during each gating period T" is then given by the relationship EQU N"=(T"/t")=(T"/R".multidot.C.multidot.Q") (4)
Theoretically, therefore, the network resistance R' is directly proportional to the pulse count N' in the first instance, represented by equation (2), whereas the network resistance R" is inversely proportional to the pulse count N" in the second instance, represented by equation (4).
As a practical matter, however, this proportionality does not strictly hold true. Parasitic line impedances, in particular, influence the time constant of the switchable RC network and thus tend to falsify the results of comparison of the pulse counts obtained with the calibrating and the unknown resistance. The effects of this measuring error are, of course, more aggravated as the ratio T/t is increased in order to provide a higher degree of resolution.